Some amount of color variation is inherent in all printing processes. Inkjet printing is no exception.
Many sources of color variation have been characterized. The two most important of these appear to be dot-size variations and hue variations.
The first of these, variation in dot size, is largely due to drop-weight variation or dot-gain variation. The second, hue variation, is sometimes due in turn to dot-size variation—but perhaps more sensitively to environmental ink-to-media interactions.
(a) Graphic-arts requirements—Consistency of color reproduction is important in all printing processes, but particularly so in production or commercial work. Accordingly for incremental printers that are designed especially for commercial use, it is especially important to control reproduction of color via closed-loop measurement and correction.
Color consistency or reproducibility, i.e. precision, is a different matter from color accuracy—although as usual accuracy is in principle attainable only to the extent that there is precision. Accuracy is related to precision as a mean value or time average 11 (FIG. 1) of a varying parameter 12 is related to the extent 13 of variation.
For a modern-day printing product, particularly in the multitasking environment, color performance immediately after calibration is limited by the I. C. C. profile capability. (The initials “I. C. C.” stand for the “InterColor Consortium”, which has developed the industry-standard “profile” or color-mapping protocol for converting input image file data, e.g. a TIFF file, into device CMYK values, with correction for color differences.)
For the statistical 95% confidence level throughout the printer gamut and product line, a mean-accuracy goal (FIG. 2) is dE=4. (The notation “dE” is a shorthand for dE*ab, which is the root-mean-square Euclidean distance between two colors in the L*a*b* color space.) Correspondingly a total color error (“TCE”) goal is dE=9.
Such performance requires that the degree of consistency in color accuracy possess a robustness to all the possible sources of color variation from the nominal. This includes changes in environment, printheads, media lots and so forth. Some of these changes typically introduce color variations so large as to swamp out all calibration efforts, and therefore simply constitute a requirement for recalibration.
Furthermore, once again, such achievement is assumed to be available only within a limited time after calibration. Hence a user who relies upon a printer for a livelihood—e.g. a graphic-arts professional—should be warned to perform the calibration on a regular basis, to keep the machine within the goals indicated. In view of these considerations, assuming full-time use, color calibrations are required weekly and also at each change of printhead or media.
(b) Related work in the art—Recent efforts by others have attacked problems of reliable field linearization in an incremental printer using a so-called “line sensor”—already present in the printer for use in interhead alignment and the like—in color-tone pseudodensitometry. Though the linearization is a field operation, a groundwork for these procedures begins with calibration of the sensor itself, preferably treated as media-independent calibration and performed at the factory.
(In some variants, a sensor calibration can be obtained with no field measurements at all—and therefore can be performed in the field, using tabulations of those colorant properties, or can simply be loaded into the printer as a complete calibration data set. Such calibration is based upon known spectral properties of the colorants that are loaded into the printer. Either the colorant properties or the calibration data as such can be, for instance, downloaded from the printer manufacturer via the WorldWide Web.)
Thereafter, with a line sensor precalibrated, linearization proceeds in the field by automatic printing of a tonal ramp, and using that sensor to measure the printed ramp. The linearization also includes—first for black-and-white colorant measurements—normalizing the sensor readings with respect to the tonal range between reflection from unprinted printing medium and the nominal maximum black tone.
Measurements of reflection from the unprinted medium are adequately precise and accurate, particularly in view of the advantageously high light level and therefore good signal-to-noise ratio for such measurements. Somewhat the contrary is the case of determinations at the other end of the printer dynamic range, where the light level in a black tone is by definition extremely low.
As a practical matter, fortunately, this black tone may in fact be treated as zero signal in the sensor. Alternative assumptions about its level may be made instead, to cope with the very great difficulty of accurately measuring, with pseudodensitometric equipment, the very low light levels involved. (For example the system may sense a dark region provided in the printer for the purpose.) In any event the normalized sensor gray-scale pseudodensitometric readings are called “absolute contrast ratios”, abbreviated “ACR”.
As to chromatic-colorant measurements, however, maximum-saturated chromatic tones cannot be considered equal to zero in light level and cannot otherwise readily be fixed to any alternative true standard. Therefore the conventional field linearization has simply proceeded on the assumption that those maximum chromatic-colorant tones are correct—and accordingly that each such tone should and must merely be accepted, as-is, to form one established endpoint of the tonal range to be linearized.
In effect the operation of each printhead was itself accepted as defining a color standard. Unfortunately, in the incremental-printing field printheads and inks are subject to significant tolerances in several parameters, leading to corresponding variations in inking density as among inks, printheads and therefore printers in a product line.
Nevertheless conventionally these chromatic-colorant measurements are followed by normalization with respect to the tonal range between reflection from unprinted print medium and the actually measured nominal maximum chromatic-colorant tone. These normalized values are called “local contrast ratios”, abbreviated “LCR”.
In some such linearization procedures, the normalized chromatic tones (which as noted above are inaccurate due to product tolerances and absence of a pertinent color standard) may further be referred to the black-and-white normalized values, which in turn are somewhat unreliable because of the above-mentioned assumptions in dealing with the black level.
Based upon nonlinearity in the normalized, adjusted and referred readings, these earlier procedures continue with determination of a correction function needed to establish linearity in the readings. They then store the correction function for use as a calibration of the printer in subsequent printing.
Such methods are adequate to correct for life effects and other variabilities that may occur among different sensors, in the absence of an on-line characterization for each individual sensor. For linearization purposes alone, they are sufficient.
Due to the limitations noted above, although the pseudodensitometric sensor systems can respond to relative tonal differences they are not capable of reliable absolute tonal readings. Accordingly these earlier systems yield reasonably well linearized hardcopy printouts but not absolute consistency—particularly not reliable consistency as among different printers, different printheads or different ink sets.
Methods described in the foregoing discussion have been introduced for printers in certain specialized markets. These include, in particular, machines for printing high-quality images of photograph-like subject matter.
Such devices are generally outfitted with correspondingly specialized printheads—e.g., in some cases, heads selected for extremely high uniformity of inkdrop weight. In some cases the printheads may be in matched sets of different colorants to be used together.
Those specialized printers are used only for art-quality reproductions, fine posters and the like. Therefore the additional cost of selected and even matched heads is readily justifiable.
Another approach that may be justified for specialized, high-end machines is provision of a fully qualified onboard colorimeter—as suggested, for example, by the previously mentioned patent document of Baker. It will be understood, however, that neither the expense of matched heads nor that of built-in colorimetry is normally acceptable in machines for regular commercial work.
Still another design philosophy is that taught by Bockman and Li in their patent document mentioned earlier. That philosophy calls for memorization of a large number of device color states distributed substantially throughout the color-solid gamut or the apparatus.
This philosophy too clearly is suited only for a relatively specialized and relatively high-end system. Even so, retention of that rather monumental amount of data does not alone necessarily ensure absolute uniformity of the rendered colors as among different unit printers of the product line.
(c) A more-demanding context—In another printing environment, particularly for use in multitasking machines such as designed for very-short-run commercial printshops, the normalization and linearization procedures outlined above would result in a greater error, which would be unacceptable for routine commercial work. One major reason for this is that in the highly competitive multitask market inkjet dropweights are substantially more variable.
In particular whereas nominal dropweight in such a machine may be 3.25 ng, economic considerations dictate that production tolerances in nozzle, heater, firing chamber and ink characteristics permit high-weight values as great as 4.5 ng. Such dropweights produce correspondingly elevated dot sizes and accordingly—when such dots merge on the printing medium—maximum tones that are subject to a magnified luminosity error 15 (FIG. 3).
For the dropweight variation just specified, this error is roughly 5 dL* units. The tone density is higher than nominal, and luminosity accordingly 5 units lower. This is an example of system performance if doing only primary linearization.
In the graph, the curved lines 16, 17 exhibit the raw LCR data for the nominal-dropweight and high-dropweight printheads respectively. In other words, these curved lines 16, 17 represent the intrinsic or natural responses of the apparatus, and most particularly of area-filling geometries for different ratios of inkdrop diameters to the spacing-apart of inkdrop centers. These area-filling geometries are further perturbed and greatly complicated by divergent coalescence behavior of different-size inkdrops, and of inkdrops on different printing media, and of inkdrops under various operating conditions.
The distance between inkdrop centers is defined by pixel dimensions. These pixel definitions in turn are set by two sets of machine operating parameters:                (1) the firing frequencies along each row—thus establishing pixel-column spacings—and        (2) printing-element spacing along the print-element arrays, and print-medium advance distance—which establish pixel-row spacings.Unfortunately the geometrical relationships between inkdrop areas and spacings cause printed tonal ramps to be nonlinear in tonal steps, even when the nominal inking density—as defined in terms of fractions of pixels inked—is increased in linear steps with a single drop diameter.        
Not only are the relationships between pixel-fraction inking and actual area coverages nonlinear, due to these geometrical factors, but in addition the specific nonlinear behavior itself varies with inkdrop diameter. This is the reason for the difference in endpoints 62, 64 of the natural response curves 16, 17 obtained for data from two printheads with different dropweights.
The luminosity discrepancy 15 appears at the low-luminosity end 62, 64 of the printer dynamic range—i.e. the high-density operating cutoff points. This is so even though at the high-luminosity end 69 the same curves 16, 17 are aligned.
The dashed straight lines 18, 19 exhibit the results of linearizing those two data sets with the nominal- and high-dropweight printheads respectively. Earlier artisans in this field—particularly in the related work discussed in subsection (b) above—have substituted these rectilinear responses 18, 19 are substituted for the intrinsic or natural curvilinear responses 16, 17 of the apparatus, by preadjusting the image data (before print-masking).
Those substitutions were definitely beneficial. They are a fundamental first step toward systematic control of colorimetric linearity in primary colors—and thereby toward orderly combinations and relationships among the secondary and other constructed colors that result from grouping primary-ink dots together. The color-combining properties articulated by Grassman's laws, and assumed in maneuvering within color space, rely upon such linearity.
Such preadjustments can be first grasped at a conceptual, graphic level as application of a conversion function 61, 63 (FIGS. 4 and 5) that is simply complementary to the intrinsic or natural transfer function 16 or 17, respectively of the apparatus. This conceptual representation resides in the generally symmetrical shape of the conversion functions 61, 63 relative to the natural response functions 16, 17 respectively—particularly when viewed as referred to the desired ideal straight-line responses 18, 19 respectively. Curves for the conversions 61, 63 are upward-concave; for the natural responses 16, 17, -convex.
To promote this conceptual understanding, in FIGS. 4 and 5 the correction functions 61, 63 are positioned in alignment with the original, natural responses 16, 17. In particular, in the nominal-dropweight case both the original response 16 and the corresponding correction function 61 diverge from a first common, high-luminosity point 69.
They reconverge at the low-luminosity ends in a second common point, the high-density cutoff 62. Analogously in the high-dropweight case both the original response 17 and corresponding correction function 63 diverge from a first common, high-luminosity point 69 and reconverge in a common low-luminosity cutoff point 64.
There is, however, no crosstalk, or causality as between the two cases. That is to say, nothing in either FIG. 4 or FIG. 5 has any influence on phenomena graphed in the other of these two illustrations.
In these conceptual illustrations (which are not to scale) the magnitudes of the corrections actually are represented by the differences between the correction functions 61, 63 and the ideal, rectilinear functions 18, 19. (This is roughly only half the difference between the illustrated correction functions 61, 63 and the natural responses 16, 17.)
A somewhat more quantitative grasp (though still not to scale) of the correction functions 61, 63 may be obtained by considering the same two functions shown alternatively as additive signal corrections ΔS and multipliers M (FIG. 6). As a practical matter, these corrections can in fact be readily derived and then applied either as additive functions ΔS, 61, 63 or as multiplicative functions M, 61, 63.
Thus the additive adjustments ΔS are pictured here as referred to a zero (0.0) baseline, whereas the multipliers M are shown referred to a unity (1.0) baseline. In each of these two cases, the right-hand (high nominal density) end of the correction curve 61 or 63 ends at the same level (0.0 or 1.0 respectively) as the left-hand (low nominal density) end.
In either event the correction terms ΔS or correction factors M do not represent mere observed errors or desired compensations. Rather these quantities are physically applied to modify input image data before halftoning—to effectuate an actual and precise linearization within the operations of a given single printer.
No such linearization, however, can cure the problem of the endpoint or cutoff-point divergence 15 (FIG. 3). This degree of divergence is readily noticeable even in a single-primary-colorant region of an image.
If such a single primary colorant is combined with another primary, this divergence goes far beyond being readily noticeable, and can be extremely conspicuous in terms of hue distortions. It is particularly conspicuous if the dropweight of that other colorant is nominal or relatively low.
Another factor that greatly exaggerates tonal error due to dropweight variation is use of so-called “light” inks: for example, light magenta or light cyan. For such colorants a curve of luminosity vs. colorant pixel density ends at various points, without at all approaching a saturation point for the full-strength colorant—i.e. any tone corresponding to an almost-constant L* value.
Using such inks, no approximation or simplification is available to circumvent the tonal and hue errors that can survive these earlier linearization systems. The distribution of errors considered statistically—in particular the 95% error, would also be roughly 5 dL*.
(d) Conclusion—Thus color inconsistencies among different printers within a single product line have continued to impede achievement of uniformly excellent inkjet printing—at high throughput—on all industrially important printing media, but still at minimal cost such as associated with a low-end multitasking printer. Thus important aspects of the technology used in the field of the invention remain amenable to useful refinement.